Strong Spin-orbit Coupling System:First Principles Study

Spin-orbit coupling (SOC) is derived from the relativistic effect that provides an interaction between orbital angular momentum and electron spin in atoms. The SOC is often considered as a small perturbation in the discussion of electrons in solids. However, in the heavy elements’compound, the SOC can not be ignored, due to the strength of SOC increasing proportionally to Z4,where Z is the atomic number. Since 2005, Kane et. al. found that the SOC can introduce the topological phase transition between trivial insulator and topological insulator, SOC become more and more im-portant in condensed matter physics. Comparing with 3d and 4d system,5d transition compounds have more extended 5d orbits which also reduce the electron-electron in-teraction (U). As a result, one can expect that the 5d transition compounds have higher metallicity and less magnetic instability. Surprisingly, some compounds which contain 5d transition elements are Mott insulators. This is because that the SOC of 5d elements are larger than that in 3d and 4d systems. Undering the interaction and competing be-tween SOC and Coulomb repulsion (U),5d transition compounds have exotic physical properties, including Mott insulator, geometrically-frustrated magnetism, topological insulator, Weyl semimetal. For heavy elements with p orbits also has strong SOC, like Bi, Pb, Te, Sb, Sn and so on. A lot of topological insulator materials contain these elements, say, HgTe/CdTe quantum well, Bi2Se3. However, topological metal also has been proposed include Dirac semimetal, Weyl semimetal and node-line semimetal. Dirac semimetal and Weyl semimetal has finite crossing point distributed at separate K points in momentum space. They have the special Fermi surface state:Fermi arc. When the time reversal symmetry or inversion symmetry broken, Dirac point would be evolve into two Weyl points with opposite chirality. The band crossing points in node-line semimetal form a line in momentum space. The surface state of node-line is two dimensional (2D) flat band. Such 2D flat band surface state is proposed as a route to achieving high temperature superconductivity. Searching the materials with strong SOC and investigating the physical properties in them are very important and significant for theoretical and experimental research. Based on first principles the-ory, tight-binding method and k-p method we have investigated several materials with strong SOC:1. we comprehensively investigate the electronic and magnetic properties of the 5d transition compound NaOsO3. We find that NaOsO3 is a new three dimensional Slater insulator. Despite of the large strength of spin-orbit coupling, it has only small effect on the electronic and magnetic properties of NaOsO3. On the other hand, the on-site Coulomb repulsion affects the band structure significantly, but a reasonable U alone cannot open a band gap. Its magnetism is itinerant, and the magnetic configuration plays an important role in determining the electronic structure. Its ground state is of a G-type antiferromagnet, and it is the combined effect of U and magnetic configuration that results in the insulating behavior of NaOsO3.2. Combining first principles calculations and effective model analysis, we predict that compounds BaYBi (Y= Au, Ag and Cu) are Dirac semimetals. These compounds are stable in the air and non-toxic, result in the potential application in experimental investigation. The electronic structure of BaCuBi is similar to BaAgBi. The band inversion happened on the Γ point between 5s state of Ag and 6p state of Bi due to strong SOC. However the band inversion of BaAuBi is happened on A point between 6p states of Bi atoms. As for the magnetic compound EuYBi, although the time reversal symmetry is broken, their long-range magnetic ordering cannot split the Dirac point into pairs of Weyl points. However, we propose that partially substitute Eu ions by Ba ions will realize the Weyl semimetal.3. We calculate the electronic structure and (001) surface states of Weyl semimetal NbP. NbP is one of the new Weyl semimetal family of TaAs. When the SOC ignored, there are node-line emerged due to the mirror symmetry. these node-lines would evolve into a pair of Weyl point when the SOC was included. Combining our first principles calculations and experimental results, we identify the existence of the Fermi arcs orig-inated from topological surface states. Furthermore, the surface states exhibit circular dichroism pattern, which may correlate with its non-trivial spin texture. Our results provide critical evidence for the existence of the Weyl Fermions in NbP, which lays the foundation for further research.4. Combining first principles calculations and effective model analysis, we pro-pose that CaTe are topological node line semimetal when SOC is ignored. When the SOC is included, three line nodes become a pair of Dirac points along the M-R line. This pair of Dirac points are protected by C4 rotation symmetry along the M-R line. When the C4 rotation symmetry is broken, like by strain effect, the Dirac semimetal will evolve into strong topological insulator. The (001) surface states of topological node line are also calculated. Its characteristic surface, namely, "drumhead" like state is also found on (001) surface.